There are various ways to solve a problem. Remember if there is a problem there is a solution.

I personally have not walked on all the paths but what I have observed and got result in solving my problems only that I can tell you because I have experienced it personally.

I have walked of the path of mantras which gave me results let me first give you my few personal experiences.

1. In my childhood I was not bright in studies. On my Grandfathers suggestion I did 1,25,000 times Gayatri Mantra. After that I cleared my Graduation and entered I.T. filed and became a Network Security Engineer. After that joined I.I.H.T. as a teacher.

I had met with many accidents in the past and so I did Maha Mrityunjay Beej Mantra 1,25,000 times after which accidents stopped happening to me.

One day I was driving my car from Gondal (Gujarat) to Ahmedabad (Gujarat) all alone. I was a lot tired and while driving my car I fell asleep. I can recall that I had left Rajkot (Gujarat) and from there I went to sleep and when I woke up I realized that I was near Sanand which is around 207 Kms away from Rajkot.

I used to do a lot of night driving and it has happened to me 3 to 4 times that I had fallen asleep while driving my car while driving but no accident ever happened to me. Now I have stopped driving at night.

I cannot share all my experiences but, I observed from my above experiences that when I did Gayatri mantra it didn’t happen that Goddess Gayatri came with Vedas in her hands and taught me Vedas rather than that some where the Gayatri Mantra increased my learning capabilities.

About my falling asleep while driving I personally don’t believe that Lord Shiv came and started to drive my car but some where I feel that because of the vibration of mantras some nodes of my brain got activated and my sub conscious mind took over and started driving when I was asleep while driving.

This is what mantras do it works on sub conscious level. We don’t even know and things start to work on its own.

I personally met many Neurologist but no one has any answers and above all they don’t have advanced machines to scan my brain and see which parts of my brain has experienced changes after my doing 1,25,000 times mantras.

There are many mantras which I have done and I have got results. For every problem there is a different mantra the only thing is that we have to do it with certain rules in order to receive its power.

Before chanting mantra it is very important to take sankalp (The sankalp has your introduction, the duration or number of mantras that are to be read, the purpose of it, all said in detail).

The method of doing 1,25,000 mantras with rules is known as Anushthan which has to be completed in 40 days. On completion of Mantra chanting, one should perform 'Dashansh Hawan' i.e. 10% Ahutis of total mantra jap done e.g. you have done 1,25,000 jap hence 1,25,000 * 10 / 100 = 12,500 ahuti and then and only then the process of Anushthan is considered to be successfully completed.

Essential requirements during anushthan :

1. Follow celibacy
2. Avoid gossips and practice silence (maun)
3. Avoid non vegetarian food and liquor
4. Fix time and place for prayer in morning and evening
5. Do not involve mind unnecessarily on worldly things
6. Keep surroundings clean
7. Be observant of mistakes
8. Do not divert your mind towards unnecessary and useless thoughts
9. Do not say any abusive words to anyone or speak lies
10. Replete your mind with reverence, faith and devoutness during the entire process
11. Do not keep on thinking every time regarding the result of Anushthan
12. At the time of idolizing, there should not be any kind of disturbance like getting up from the worship place again and again, attending phone calls in between etc.
13. There should a fixed for eating and one should consume light food at fixed time
14. Refraining from leather-ware like shoes etc

Few mantras which can be used to solve your common problems :

1. Ganpati Mantra - Om Vakratundaya Hum
This is a powerful mantra from Ganesha Purana. When things are not in your favour, or when the minds of the people turn negative, depressed or discouraged, the attention of Ganesha may be drawn by this mantra to straighten their ways. The HUM symbolizes "Delay no more, my Lord, in straightening the paths of the crooked-minded ones." This mantra is used many a times in the Ganesha Purana to reduce the violence of cruel demons.
2. Gayatri Mantra - Om Bhur Bhuvah Swaha Tat Savitur Varenyam Bhargo Devasya
                       Dhimahi Dhiyo Yo Nah Prachodyat
Chanting of Gayatri Mantra removes all obstacles in our path to increased wisdom and spiritual growth and development.Righteous wisdom starts emerging soon after Jap (recitation) of the Gayatri Mantra is performed.Sathya Sai Baba teaches that the Gayatri Mantra will protect you from harm , make your intellect shine, improve your power of speech, and dispel the darkness of ignorance.
3. Maha Mrityunjay Beej Mantra - Om Tryambakam Yajamahe Sugandhim Pushtivardhanam
                                          Urvarukamiv Bandhanan Mrityor Mukshiya Maamritat
The Mahamrityyunjaya mantra, also called the Markandeya Mantra, is considered to be the greatest healing mantra. It cures ailments, disease and poor health and also bestows a person with health, wealth and power. It saves the Sadhaka from untimely death or Akal Mrityu.
4. Hanuman Mantra - Om Hum Hanumate Rudratmakaya Hum Phat Swaha
The Hanuman mantras are very effective for all Saturn related problems, for health, to avoid and overcome troubles caused from enemies and to avoid imprisonment.

Rest there are a lot of mantras which you can easily get from internet or a saint.

Mantras of planets and its jap sankhya :

1. Surya - Om hram hreem hroum sah suryaya namah
  7000 Jap * 4 kalyug = 28000
2. Chandra - Om shram sreem shrom sah chandraya namah
  11000 Jap * 4 kalyug = 44000
3. Mangal - Om kram kreem kroum sah bhomaya namah
  10000 Jap * 4 kalyug = 40000
4. Buddh - Om bram breem broum sah budhaya namah
  4000 Jap * 4 kalyug = 16000
5. Guru - Om gram ghreem groum sah gurave namah
  19000 Jap * 4 kalyug = 76000
6. Shukra - Om dram dreem droum sah shukraya namah
  16000 Jap * 4 kalyug = 64000
7. Shani - Om pram preem proum sah shanaischaraya namah
  23000 Jap * 4 kalyug = 92000
8. Rahu - Om bhram bhreem bhroum sah rahave namah
  18000 Jap * 4 kalyug = 72000
9. Ketu - Om shram shreem shroum sah ketave namah
  17000 Jap * 4 kalyug = 68000

The jap should be completed in 40 days and most important thing is that you will only get the result when you yourself do the jap.

One important thing to note is that if a person starts to do wrong things in his life like lying, cheating, using foul language, misuses power, etc. then power achieved through jap reduces and finally vanishes.